Joint monarchs (biarchs?) of England, William III of Orange and Mary II of Stuart. Mary was the (Anglican; this is important) daughter of James II. William was stadtholder of the Netherlands. As was common in European aristocracy of those days, they were first cousins: William was the son of James II's sister Mary. (*)

In 1688, Parliament appealed to William III of Orange to help protect England from a Catholic takeover (the King, James II, as well as his heir apparent, were Catholic). He invaded in November 1688, triggering the Glorious Revolution and James' abdication.

Parliament wanted Mary to have the throne, with William as Prince Consort; she refused (because of her self-imposed subservience to William). William did not want to take the throne by conquest, but preferred to be named King by birthright. Parliament eventually acceded, and the two came to rule jointly.

During the reign of William and Mary (and, after Mary's death, William alone), Parliament did much to weaken the Crown. First the Bill of Rights, then the Mutiny Act and Settlement Act, established Parliament's supremacy.

Mary died childless in 1694. Since it appeared William would leave no heirs, and since Parliament would stop at nothing to prevent a Catholic from taking the throne again, the Settlement Act of 1701 barred James II's two Catholic children (James Francis Edward Stuart, Prince of Wales; and Louisa Maria Theresa Stuart) from the throne. It also stated that, should the eligible Stuart line expire (it seemed it would, as the only surviving Protestant child of James II was Anne Stuart, all of whose children had died by the age of two), the throne should devolve on the descendents of Charles I's granddaughter Sophia Hanover. When William died in 1702, the crown passed to Anne, Queen of England, the last Stuart monarch. On her death in 1714, the Settlement Act took effect, and George, Elector of Hanover became King George I, the first British monarch of the Hanover dynasty.

(*): Thanks for Gorgonzola for pointing out that William and Mary were first cousins.